Liquid State Machine Research Articles

Chaotic Liquid State Machine

The authors implement a Liquid State Machine composed from a pool of chaotic spiking neurons. Furthermore, a synaptic plasticity mechanism operates on the connection weights between the neurons inside the pool. A special feature of the system's classification capability is that it can learn the class of a set of time varying inputs when trained from positive examples only, thus, it is a one class classifier. To demonstrate the applicability of this novel neurocomputing architecture, the authors apply it for Online Signature Verification.

Non-parametric temporal modeling of the hemodynamic response function via a liquid state machine

Standard methods for the analysis of functional MRI data strongly rely on prior implicit and explicit hypotheses made to simplify the analysis. In this work the attention is focused on two such commonly accepted hypotheses: (i) the hemodynamic response function (HRF) to be searched in the BOLD signal can be described by a specific parametric model e.g., double-gamma; (ii) the effect of stimuli on the signal is taken to be linearly additive. While these assumptions have been empirically proven to generate high sensitivity for statistical methods, they also limit the identification of relevant voxels to what is already postulated in the signal, thus not allowing the discovery of unknown correlates in the data due to the presence of unexpected hemodynamics. This paper tries to overcome these limitations by proposing a method wherein the HRF is learned directly from data rather than induced from its basic form assumed in advance. This approach produces a set of voxel-wise models of HRF and, as a result, relevant voxels are filterable according to the accuracy of their prediction in a machine learning framework.This approach is instantiated using a temporal architecture based on the paradigm of Reservoir Computing wherein a Liquid State Machine is combined with a decoding Feed-Forward Neural Network. This splits the modeling into two parts: first a representation of the complex temporal reactivity of the hemodynamic response is determined by a universal global “reservoir” which is essentially temporal; second an interpretation of the encoded representation is determined by a standard feed-forward neural network, which is trained by the data. Thus the reservoir models the temporal state of information during and following temporal stimuli in a feed-back system, while the neural network “translates” this data to fit the specific HRF response as given, e.g. by BOLD signal measurements in fMRI.An empirical analysis on synthetic datasets shows that the learning process can be robust both to noise and to the varying shape of the underlying HRF. A similar investigation on real fMRI datasets provides evidence that BOLD predictability allows for discrimination between relevant and irrelevant voxels for a given set of stimuli.

A Digital Liquid State Machine With Biologically Inspired Learning and Its Application to Speech Recognition.

This paper presents a bioinspired digital liquid-state machine (LSM) for low-power very-large-scale-integration (VLSI)-based machine learning applications. To the best of the authors' knowledge, this is the first work that employs a bioinspired spike-based learning algorithm for the LSM. With the proposed online learning, the LSM extracts information from input patterns on the fly without needing intermediate data storage as required in offline learning methods such as ridge regression. The proposed learning rule is local such that each synaptic weight update is based only upon the firing activities of the corresponding presynaptic and postsynaptic neurons without incurring global communications across the neural network. Compared with the backpropagation-based learning, the locality of computation in the proposed approach lends itself to efficient parallel VLSI implementation. We use subsets of the TI46 speech corpus to benchmark the bioinspired digital LSM. To reduce the complexity of the spiking neural network model without performance degradation for speech recognition, we study the impacts of synaptic models on the fading memory of the reservoir and hence the network performance. Moreover, we examine the tradeoffs between synaptic weight resolution, reservoir size, and recognition performance and present techniques to further reduce the overhead of hardware implementation. Our simulation results show that in terms of isolated word recognition evaluated using the TI46 speech corpus, the proposed digital LSM rivals the state-of-the-art hidden Markov-model-based recognizer Sphinx-4 and outperforms all other reported recognizers including the ones that are based upon the LSM or neural networks.

Bray-Curtis Metrics as Measure of Liquid State Machine Separation Ability in Function of Connections Density

Abstract Separation ability is one of two most important properties of Liquid State Machines used in the Liquid Computing theory. To measure the so-called distance of states that Liquid State Machine can exist in – different norms and metrics can be applied. Till now we have used the Euclidean distance to tell the distance of states representing different stimulations of simulated cortical microcircuits. In this paper we compare our previously used methods and the approach with Bray-Curtis measure of dissimilarity. Systematic analysis of efficiency and its comparison for a different number of simulated synapses present in the model will be discussed to some extent.

Corrigendum to Bray-curtis Metrics as Measure of Liquid State Machine Separation Ability in Function of Connections Density

Corrigendum to Bray-curtis Metrics as Measure of Liquid State Machine Separation Ability in Function of Connections Density

Bray-Curtis Metrics as Measure of Liquid State Machine Separation Ability in Function of Connections Density

Bray-Curtis Metrics as Measure of Liquid State Machine Separation Ability in Function of Connections Density

Liquid State Machine With Dendritically Enhanced Readout for Low-Power, Neuromorphic VLSI Implementations

In this paper, we describe a new neuro-inspired, hardware-friendly readout stage for the liquid state machine (LSM), a popular model for reservoir computing. Compared to the parallel perceptron architecture trained by the p-delta algorithm, which is the state of the art in terms of performance of readout stages, our readout architecture and learning algorithm can attain better performance with significantly less synaptic resources making it attractive for VLSI implementation. Inspired by the nonlinear properties of dendrites in biological neurons, our readout stage incorporates neurons having multiple dendrites with a lumped nonlinearity (two compartment model). The number of synaptic connections on each branch is significantly lower than the total number of connections from the liquid neurons and the learning algorithm tries to find the best 'combination' of input connections on each branch to reduce the error. Hence, the learning involves network rewiring (NRW) of the readout network similar to structural plasticity observed in its biological counterparts. We show that compared to a single perceptron using analog weights, this architecture for the readout can attain, even by using the same number of binary valued synapses, up to 3.3 times less error for a two-class spike train classification problem and 2.4 times less error for an input rate approximation task. Even with 60 times larger synapses, a group of 60 parallel perceptrons cannot attain the performance of the proposed dendritically enhanced readout. An additional advantage of this method for hardware implementations is that the 'choice' of connectivity can be easily implemented exploiting address event representation (AER) protocols commonly used in current neuromorphic systems where the connection matrix is stored in memory. Also, due to the use of binary synapses, our proposed method is more robust against statistical variations.

Input coding for neuro-electronic hybrid systems

Liquid State Machines have been proposed as a framework to explore the computational properties of neuro-electronic hybrid systems (Maass et al., 2002). Here the neuronal culture implements a recurrent network and is followed by an array of linear discriminants implemented using perceptrons in electronics/software. Thus in this framework, it is desired that the outputs of the neuronal network, corresponding to different inputs, be linearly separable. Previous studies have demonstrated this by either using only a small set of input stimulus patterns to the culture (Hafizovic et al., 2007), large number of input electrodes (Dockendorf et al., 2009) or by using complex schemes to post-process the outputs of the neuronal culture prior to linear discriminance (Ortman et al., 2011). In this study we explore ways to temporally encode inputs into stimulus patterns using a small set of electrodes such that the neuronal culture's output can be directly decoded by simple linear discriminants based on perceptrons. We demonstrate that network can detect the timing and order of firing of inputs on multiple electrodes. Based on this, we demonstrate that the neuronal culture can be used as a kernel to transform inputs which are not linearly separable in a low dimensional space, into outputs in a high dimension where they are linearly separable. Thus simple linear discriminants can now be directly connected to outputs of the neuronal culture and allow for implementation of any function for such a hybrid system.

The association between cell assemblies and transient dynamics

Neural systems show a wide variety of complex dynamics on different time scales. Specifically, on the short time scale of neuronal activations (milliseconds to seconds), several theoretical models (e.g., state-dependent networks or liquid state machines [1]) demonstrate that complex (transient) dynamics enables neural circuits to process a broad range of nonlinear problems. In other words, neural circuits process inputs to transform them into desired outputs. This approach, amongst others, is based on the inherent stochasticity (randomness) of neural systems. On the other hand, the slower mechanisms of synaptic plasticity (minutes to hours) adapt synaptic efficacies to form ordered structures as neural cell assemblies [2]. Each cell assembly consists of a group of strongly interconnected neurons and its dynamics serves as an associative memory of the previously experienced input. This type of dynamics is in stark contrast to the needed randomness of connectivity for transient dynamics. Intriguingly, several experiments show that both concepts coexist in the same neural circuits [3,4]. In this study we analyze how this coexistence of transient dynamics and cell assemblies can emerge in one neural circuit. The neural network, we investigate, consists of rate- based neurons with connections adapted by a generic combination of Hebbian plasticity and synaptic scaling [5]. A subset of neurons receives repeatedly a time-varying input and forms a cell assembly (Figure ​(Figure1).1). Further repetitions of the input lead to a gradual growth of the cell assembly by incorporating more neurons. In parallel, the network is required to compute a desired nonlinear version of the input. To test whether this computation is successful, the connections between the neurons of the network and a linear output neuron are adapted by a supervised learning algorithm [6]. Remarkably, the performance of the computation increases with the growth in size of the cell assembly. Thus, the slow, ordering dynamics of synaptic plasticity supports the computational capability of the fast transient dynamics. Furthermore, as the cell assemblies are topologically compact, the network is able to perform several computations in parallel (green and red cell assemblies in Figure ​Figure1).1). However, if the cell assemblies become neighbors, dependent on the input, one cell assembly can capture neurons from the other assembly (stripped area in Figure ​Figure1).1). Thus, the cell assemblies compete for computational resources, namely neurons and synapses. Therefore, our work shows a new functional role of cell assemblies in neuronal systems, whereby both stable and transient dynamics are byproduct of the same neural circuit. Thus, both concepts are not mutually exclusive but that they interact with each other in a positive way. Figure 1 Basic setting of the system. CAi: Cell Assembly i; Ii: Input to CAi; Oi: Output of CAi; Fi: Function processed by CAi

Liquid computing and analysis of sound signals

Liquid Computing Theory is a proposal of modelling the behaviour of neural microcircuits.It focuses on creating a group of neurons, known as a liquid layer, responsible for preprocessingof the signal that is being analysed. Specific information is achieved by the readout layers, task orientedgroups of neurons, taught to extract particular information from the state of liquid layer. TheLSMs have been used to analyse sound signals. The liquid layer was implemented in the PCSIM Simulator,and the readout layer has been prepared in the JNNS simulator. It could successfully recognisecertain sounds despite noises. Those results encourage further research of the computational potentialof Liquid State Machines including working in parallel with many readout layers.

Liquid computing and analysis of sound signals

AbstractLiquid Computing Theory is a proposal of modelling the behaviour of neural microcircuits. It focuses on creating a group of neurons, known as a liquid layer, responsible for preprocessing of the signal that is being analysed. Specific information is achieved by the readout layers, task oriented groups of neurons, taught to extract particular information from the state of liquid layer. The LSMs have been used to analyse sound signals. The liquid layer was implemented in the PCSIM Simulator, and the readout layer has been prepared in the JNNS simulator. It could successfully recognise certain sounds despite noises. Those results encourage further research of the computational potential of Liquid State Machines including working in parallel with many readout layers.

Computational capability of liquid state machines with spike-timing-dependent plasticity

Liquid state machine (LSM) is a recently developed computational model with a reservoir of recurrent spiking neural network (RSNN). This model has shown to be beneficial for performing computational tasks. In this paper, we present a novel type of LSM with self-organized RSNN instead of the traditional RSNN with random structure. Here, the spike-timing-dependent plasticity (STDP) which has been broadly observed in neurophysiological experiments is employed for the learning update of RSNN. Our computational results show that this model can carry out a class of biologically relevant real-time computational tasks with high accuracy. By evaluating the average mean squared error (MSE), we find that LSM with STDP learning is able to lead to a better performance than LSM with random reservoir, especially for the case of partial synaptic connections.

The Convallis learning rule for unsupervised learning in spiking neuronal networks

Learning is often considered to be governed by reinforcement, causing animals to increase the probability of performing rewarded behaviours, and decrease the probability of behaviours leading to harmful outcomes. However, not all learning is governed by reward. Mere exposure to a novel environment or set of sensory stimuli, unpaired with any behaviour or reinforcement, leads to perceptual learning that allows the animal to more readily form behavioural associations with these stimuli, should the need later arise. In statistics and machine learning, the problem of forming representations of a data set without any explicit training is called learning. Artificial neural networks that perform unsupervised learning have been described, primarily for the case of firing rate neurons. Many of these learning rules allow the networks to perform analyses equivalent to standard statistical techniques. For example, a variant of the Bienenstock, Cooper and Monro (BCM) theory of plasticity allows neurons to implement projection pursuit, a statistical technique for searching for non-Gaussian projections of input data. Here we describe a synaptic rule for unsupervised learning in spiking neurons. The rule is derived as gradient optimization of the time integral of a nonlinear function of membrane potential. This function is shaped like a valley, leading to a preference for membrane potentials near rest or spike threshold, but avoiding intermediate-level potentials (the name comes from the Latin for valley). To avoid saturation, the rule is stabilized by a homeostatic mechanism that enforces a constant firing rate using a PI controller that scales synaptic weights. This combination causes neurons to develop a skewed, non-Gaussian distribution of membrane potentials analogously to the projection pursuit algorithm. Using the TIDIGITS database of spoken digit utterances, we show the rule allows a recurrent network of spiking excitatory and inhibitory neurons to develop selective representations of these digits. Applying a linear classifier downstream of the recurrent network shows the Convallis rule allows substantially better readout than a purely random network (liquid-state machine), the homeostatic rule alone, or various other plasticity rules for spiking neurons. Applying the rule to simulations of in vitro plasticity paradigms, we find that it reproduces several published results including STDP, although STDP alone cannot produce similar performance in speech recognition. We suggest that ability to perform real-world information processing tasks provides a useful way to constrain theories of synaptic plasticity.

Movement Prediction using Reservoir Computing

1. ABSTRACT In this work the Reservoir Computing (RC) technique; specifically the Liquid State Machine (LSM) was chosen to simulate a Movement Predictor system at minimum cost, experiencing both short and long term prediction. Also in this work shows the possibility to simulate the LSM without the need to event based simulation (i.e. proving that it is not urgent to interface the MATLAB programming language with other programming languages like C and C to simulate the LSM). The encoding from spiking to analog domain was avoided in this work. This means there is no waste in the input information due to the encoding process. Also this will result in simpler LSM scheme.

Use of the separation property to derive Liquid State Machines with enhanced classification performance

Liquid State Machines constitute a powerful computational tool for carrying out complex real time computations on continuous input streams. Their performance is based on two properties, approximation and separation. While the former depends on the selection of class functions for the readout maps, the latter needs to be evaluated for a particular liquid architecture. In the current paper we show how the Fisher's Discriminant Ratio can be used to effectively measure the separation of a Liquid State Machine. This measure is then used as a fitness function in an evolutionary framework that searches for suitable liquid properties and architectures in order to optimize the performance of the trained readouts. Evaluation results demonstrate the effectiveness of the proposed approach.

Effects of synaptic connectivity on liquid state machine performance

The Liquid State Machine (LSM) is a biologically plausible computational neural network model for real-time computing on time-varying inputs, whose structure and function were inspired by the properties of neocortical columns in the central nervous system of mammals. The LSM uses spiking neurons connected by dynamic synapses to project inputs into a high dimensional feature space, allowing classification of inputs by linear separation, similar to the approach used in support vector machines (SVMs). The performance of a LSM neural network model on pattern recognition tasks mainly depends on its parameter settings. Two parameters are of particular interest: the distribution of synaptic strengths and synaptic connectivity. To design an efficient liquid filter that performs desired kernel functions, these parameters need to be optimized. We have studied performance as a function of these parameters for several models of synaptic connectivity. The results show that in order to achieve good performance, large synaptic weights are required to compensate for a small number of synapses in the liquid filter, and vice versa. In addition, a larger variance of the synaptic weights results in better performance for LSM benchmark problems. We also propose a genetic algorithm-based approach to evolve the liquid filter from a minimum structure with no connections, to an optimized kernel with a minimal number of synapses and high classification accuracy. This approach facilitates the design of an optimal LSM with reduced computational complexity. Results obtained using this genetic programming approach show that the synaptic weight distribution after evolution is similar in shape to that found in cortical circuitry.

Memory formation, recall and forgetting in neuronal networks

Event Abstract Back to Event Memory formation, recall and forgetting in neuronal networks Christian Tetzlaff1*, Christoph Kolodziejski2, Marc Timme2, Misha Tsodyks3 and Florentin Wörgötter1 1 University of Goettingen, Biophysics - Faculty of Physics, Germany 2 Max Planck Insitute for Dynamics and Self-Organization, Germany 3 Weizmann Institute, Israel Which processes are behind the ability of biological neuronal circuits for memory formation, recall, and forgetting (e.g., objects or facts) is still under heavy debate in neuroscience. Although several theoretical approaches exist (e.g. Hopfield networks [Hopfield, 1982], attractor networks [Mongillo et al., 2008], liquid-state machines [Maass et al., 2002]), each approach has difficulties like, for instance, arbitrary non-biological constraints (e.g. Hopfield networks), predefined connectivity (e.g. attractor networks), or supervised recall (e.g. liquid-state machines). In Tetzlaff et al., 2011 we analyzed a combination of conventional plasticity [e.g. Hebb, 1949] and synaptic scaling [Turrigiano et al., 1998] that builds up memory traces (cell assemblies) induced by external inputs. Here we show that the combination of this mechanism with a cortex-like structure can form (“learn”), retrieve and delete clusters of highly connected neurons within recurrent neuronal networks. Synapses in such a cluster are significantly stronger than those between different clusters, thus similar connectivity patterns recently observed in the cortex [Perin et al., 2011]. In our model inter-cluster connection strength directly depends on duration and frequency of the presentation of an unknown entity. Thus, for complete recall of a well-learned (often presented) entity, a smaller fraction of cluster neurons have to be stimulated and recall is quick. Well-trained clusters are not only quantitatively but also qualitatively different from sporadically-trained clusters: The time scale for forgetting the former is significantly longer than for the latter so that it takes longer to forget a well-learned entity. Synaptic scaling in combination with conventional plasticity thus leads to 1) learning of new memory entities, 2) recalling of clusters while synaptic weights remain plastic which additionally supports memory formation through relearning, and 3) forgetting, which depends on the state (well- or sporadically-learned) the cluster is in.

Electrical parameters influence on the dynamics of the Hodgkin–Huxley liquid state machine

The model of mammalian cortical hypercolumn was simulated using liquid state machines built of simple Hodgkin–Huxley neurons. The influence of cell electrical parameters on the system dynamics was investigated. The systematic analysis of the hypercolumn separation ability in the function of time constants, cell membrane capacitance, resistance, Hodgkin–Huxley equilibrium potential and sodium and potassium channel conductances was performed. Optimal ranges of time constants for the most effective computational abilities of the model were estimated.

Self-organising criticality in the simulated models of the rat cortical microcircuits

Two and three dimensional models of rat barrel and somatosensory cortex were simulated. Hoddgkin–Huxley and Leaky-Integrate-and-Fire neurons were used to the construction of the networks in GENESIS and PCSIM environments. The dynamics of both models was analysed. Self-organising criticality phenomena were found. Profound investigations of this behaviour showed its dependence not only on the number of connections, but also on the simulated network architecture originating, e.g., from varying probability of exocytosis or synapse creation in the selected areas of the network. For two dimensional model the results were compared to that obtained for smaller models and analysis of this comparison is presented to some extent. The three dimensional model of the rat primary somatosensory cortex is based on the ensemble of Liquid State Machines. The results obtained from that model are in good agreement with the dynamics recorded in neurophysiological experiments on real brain.

Unorganized Machines

This work presents a discussion about the relationship between the contributions of Alan Turing – the centenary of whose birth is celebrated in 2012 – to the field of artificial neural networks and modern unorganized machines: reservoir computing (RC) approaches and extreme learning machines (ELMs). Firstly, the authors review Turing’s connectionist proposals and also expose the fundamentals of the main RC paradigms – echo state networks and liquid state machines, - as well as of the design and training of ELMs. Throughout this exposition, the main points of contact between Turing’s ideas and these modern perspectives are outlined, being, then, duly summarized in the second and final part of the work. This paper is useful in offering a distinct appreciation of Turing’s pioneering contributions to the field of neural networks and also in indicating some perspectives for the future development of the field that may arise from the synergy between these views.